Varieties of Dirac equation and flavors of leptons and quarks

Details Varieties of Dirac equation and flavors of leptons and quarks Varieties of Dirac equation and flavors of leptons and quarks

2001-07-17

arxiv.org/abs/hep-ph/0107184v2

Physics

High Energy Physics

High Energy Physics - Phenomenology

5 pages, RevTeX

Scientific paper

I show that there exist twelve independent Dirac equations for spin 1/2 fermions. The Dirac fields that satisfy these equations can be grouped into six pairs according to the way they transform under continuous space-time transformations. These six pairs of Dirac equations correspond to the three quark generations and the three lepton generations. The charged V-A currents can be formed only from fields of the same pair. This property of the Dirac fields implies that a quark or lepton may be transformed only into its partner of the same generation via the charged-current weak interaction. According to the properties of the charged-current weak interaction, I conclude that different elementary fermion fields must satisfy different Dirac equations, and there may not be more than twelve flavors of elementary fermions that are already known.

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